Question

How is the graph of y = log (x) transformed to produce the graph of y = log (2 x) + 3?

Answer 1

Answer:

Step-by-step explanation:

The graph of log 2x has the same shape as that of log x, except that it is compressed horizontally by a factor of 2.

Additionally, that +3 indicates that we must translate the above graph upwards by 3 units.

Answer 2

we must replace $x$ by $2\cdot x$ and then translate the function 3 units in the +y direction.

We can transform $y = \log x$ into $y = \log 2\cdot x +3$ by means of the following operations:

1. Replace $x$ by $2\cdot x$. (Dilation factor: 2)
2. Translate the resulting expression 3 units in the +y direction. (Vertical translation)

That is, we represent the operations defined above mathematically:

1) $y = \log x$

2) $y = \log 2\cdot x$

3) $y = \log 2\cdot x + 3$

In a nutshell, we must replace $x$ by $2\cdot x$ and then translate the function 3 units in the +y direction.

We kindly invite to check this question on transformation rules: https://brainly.com/question/17478764